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A committe od five people is to be chosen from a club that boast a membership...

A committe od five people is to be chosen from a club that boast a membership of ten men and 12 women. how many can the committee be formed if it is to contain atleast two men and two women?how many if in addition , one particular man and one woman who are members of the club refuse to serve together on the committee?

prove that (n choose r ) = (n choose n-r) by using a combinatorial argument.
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